Titlebook: Relational Topology; Gunther Schmidt,Michael Winter Book 2018 Springer International Publishing AG, part of Springer Nature 2018 Relationa

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Prerequisites,, Fakultät für Informatik, Universität der Bundeswehr München, April 2014). There, full proofs may be found. In addition it is shown how everything is based on a concise axiomatic basis. However, some of the following results are new, and therefore given together with their proof.

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Products of Relations,In Definition ., we have introduced the direct power of a set—modelling the concept of a powerset—and shown that it is uniquely determined up to isomorphism. Even earlier, we have defined the natural projection of a set equipped with an equivalence to the set of its classes. We are now going to handle the direct product and direct sum.

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Closures and Their Aumann Contacts,Topology has been shown to be definable in several cryptomorphically equivalent ways: by a neighborhood system, by a collection of open sets (be these given as a vector along the powerset or as a partial diagonal on it), by a collection of closed sets, or by a mapping to open kernels.

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Simplicial Complexes,This section is intended to show how one might work relationally also for algebraic topology. We give a glimpse of simplicial complexes, usually subsumed under that topic.